Answer:
Given the system of equation:
[tex]2x+9y = -26[/tex] .....[1]
[tex]-3x-7y=13[/tex] ......[2]
Multiply equation [1] by -3 to both sides we get;
[tex]-6x-27y = 78[/tex] .....[3]
Multiply equation [2] by 2 to both sides we get;
[tex]-6x-14y = 26[/tex] .....[4]
Subtract equation [4] from [3] to eliminate x we get;
[tex]-6x-27y-(-6x-14y) = 78-26[/tex]
[tex]-6x-27y+6x+14y= 78-26[/tex]
Combine like terns we get;
[tex]-13y = 52[/tex]
Divide both sides by -13 we get;
y = -4
Substitute the value of y in equation [1] we get;
[tex]2x+9(-4) = -26[/tex]
[tex]2x-36 = -26[/tex]
Add 36 to both sides we get;
2x = 10
Divide both sides by 2 we get;
x = 5
Therefore, the solution for the system of equation is (5, -4)
